THE COMPARISON OF THE METHODS ESTIMATING THE FRACTIONAL DIFFERENCES OF PARAMETER AND ITS DEPENDENCE ON ESTIMATION THE BEST LINEAR MODEL OF TIME SERIES IN THE ENVIRONMENTAL FIELD

Journal > Journal > Journal Vol – 15 No -8, August 2020 > THE COMPARISON OF THE METHODS ESTIMATING THE FRACTIONAL DIFFERENCES OF PARAMETER AND ITS DEPENDENCE ON ESTIMATION THE BEST LINEAR MODEL OF TIME SERIES IN THE ENVIRONMENTAL FIELD

August 21, 2020

Journal Vol – 15 No -8, August 2020

Authors:

Saad Kazem Hamza,Shareen Ali Hussein,

DOI NO:

https://doi.org/10.26782/jmcms.2020.08.00014

Keywords:

ARFIMA (p,d,q) models,long term memory,smoothed periodogram method,air pollution,spectrum function,

Abstract

This paper exploring the stability to be achieved in the stochastic processes and operations which are called the autoregressive moving average and symbolized by ARMA Model(the roots of the equation should be out of this model circle.  Although these models are not stable and become stable after so many conversions and differences. These new models called the autoregressive methods for integrated moving average which is symbolized ARFIMA (p, d, q) and these differences would be integers or fractional numbers. It is worth to be mentioned that the time series which depending on the long term (long memory) so this stability achieved by snapping the fractional differences which are located within the enclosed period (-0.5, 0.5) and are referred shortly ((ARFIMA (p,d,q))). Models which are located within the enclosed period (-0.5, 0.5). This search aims to estimate the parameter of fractional differences (d), three ways by using real data from the Ministry of Environment that include the rates of air pollution in Baghdad City with Nitrogen oxides(NO²), Ozone(Oᶟ) materials…these ways are: firstly, the way logarithm periodogram chart regression method which is called (Geweke and Porter- Hudak), symbolized (GPH) Secondly, smoothed periodogram regression. Thirdly, the way that called (KASHYAP AND EOM) and it has been used the standard error squares and standard error (SD) as two scale standards among these three ways to estimate the parameter. Akaike standard has been used for choosing the best model of linear models assumed.In this study, we will be dealt with the fractional differences

Refference:

I. Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics. Journal of Econometrics,73(1), 5-59. doi:10.1016/0304-4076(95)01732-1

II. Franco, G. C., & Reisen, V. A. (2007). Bootstrap approaches and confidence intervals for stationary and non-stationary long-range dependence processes. Physica A: Statistical Mechanics and Its Applications,375(2), 546-562. doi:10.1016/j.physa.2006.08.027

III. Hassler, U. (1993). Regression of Spectral Estimators with Fractionally Integrated Time Series. Journal of Time Series Analysis,14(4), 369-380. doi:10.1111/j.1467-9892.1993.tb00151.

IV. Karemera, D., & Kim, B. J. (2006). Assessing the forecasting accuracy of alternative nominal exchange rate models: The case of long memory. Journal of Forecasting,25(5), 369-380. doi:10.1002/for.994

V. KASHYAP,R.L. and EOM,B.(1988) Estimation in long memory time series models J.time series Anal.9,35-41 long-memory parameter”.Department of Statistics, UFES, ES, UFMG, MGBrazil.

VI. Mandelbrot, B. B., & Wallis, J. R. (1968). Noah, Joseph, and Operational Hydrology. Water Resources Research, 4(5), 909-918. doi:10.1029/wr004i005p00909

VII. Ministry of Environment, records Waziriya station, daily readings of the station during the days of actual work for two years 2017.2018, Iraq – Baghdad 0.2019.

VIII. Porter, Hudak, S. (1982). Long – Term Memory: Modelling A simplified Spectral Approach. Unpublished Ph.D Dissertation, University of Wisconsin

IX. Reisen, V. A., Cribari-Neto, F., & Jensen, M. J. (2003). Long Memory Inflationary Dynamics: The Case of Brazil. Studies in Nonlinear Dynamics & Econometrics,7(3). doi:10.2202/1558-3708.1157

X. Reisen.V.A. (1993) “Estimation of the fractional difference parameter in the ARIMA(p,d,q) model using the smoothed periodogram”. Journal of time series analysis .Vol.15,No.3.

XI. Reisen.V.A.&Franco.G.C.(2006).”Log average sample spectral estimators oflong-memory parameter”.Department of Statistics, UFES, ES, UFMG, MGBrazil.

XII. RichardT.Baillie (1996) “long memory processes and fractional integration in econometric” department of Economics,Michigan state university,USA.

XIII. Wei, William W. S. – 1990 – (Time Series Analysis) – Addison – Wesley publishing Company p:278.

XIV. Wilkins, N. (2003). Fractional Integration at a Seasonal Frequency with an Application to Quarterly Unemployment Rates. School of Finance and Economics University of Technology, Sydney, 1-32.

View Download